Number problems at primary level that require careful consideration.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you substitute numbers for the letters in these sums?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
What is happening at each box in these machines?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Use the number weights to find different ways of balancing the equaliser.
Are these domino games fair? Can you explain why or why not?
Who said that adding couldn't be fun?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
If you have only four weights, where could you place them in order
to balance this equaliser?
Number problems at primary level to work on with others.
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This challenge is about finding the difference between numbers which have the same tens digit.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
This dice train has been made using specific rules. How many different trains can you make?
Can you hang weights in the right place to make the equaliser
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Number problems at primary level that may require determination.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Got It game for an adult and child. How can you play so that you know you will always win?
An environment which simulates working with Cuisenaire rods.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Noah saw 12 legs walk by into the Ark. How many creatures did he see?